There are two frameworks in which the above Motto can be translated into a precise Theorem: the first framework is logarithmic geometry, and the second one is non-Archimedean analytic geometry (a la Berkovich). In the non-Archimedean analytic framework, a part of this Motto involving special types of stability conditions has already been realized in [1]} (see Theorem REF  below and the discussion right after). In the logarithmic framework, and in the non-Archimedean one in the absence of stability conditions, our results appear to be new.
